Stereotactic Body Radiation Therapy With REGN2810 and/or Ipilimumab Before Surgery in Treating Participants With Progressive Advanced or Oligometastatic Prostate Cancer

Inclusion Criteria: * Be willing and able to provide written informed consent for the trial * Have progressive advanced prostate cancer based on at least one of the following criteria: * Gleason score of ≥ 7 * Any PSA * TNM clinical stage T3-T4, N1 * Oligometastatic prostate cancer patients who have not received primary therapy are eligible; (oligometastatic disease is defined as a patient with ≤ 3 metastatic bone lesions on the bone scan or tissue metastasis) * To be scheduled for a Radical Prostatectomy * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) ≥ 1000 /mcL within 7 days of treatment initiation * Platelets ≥ 150,000 / mcL within 7 days of treatment initiation * Hemoglobin ≥ 9 g/dL or ≥ 5.6 mmol/L within 7 days of treatment initiation * Lymphocytes ≥ 500 / mcL within 7 days of treatment initiation * Serum creatinine ≤ 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance (CrCl) ≥ 50 mL/min for subject with creatinine levels \> 1.5 X institutional ULN within 7 days of treatment initiation \* Glomerular filtration rate (GFR) can also be used in place of creatinine or CrCl * Serum total bilirubin ≤ 1.5 X ULN within 7 days of treatment initiation \* Direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 ULN within 7 days of treatment initiation * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 2.5 X ULN within 7 days of treatment initiation * International normalized ratio (INR) or prothrombin time (PT) ≤ 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or INR is within therapeutic range of intended use of anticoagulants within 7 days of treatment initiation * Activated partial thromboplastin time (aPTT) ≤ 1.5 X ULN unless subject is receiving anticoagulant therapy as long as aPTT is within therapeutic range of intended within 7 days of treatment initiation Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent within 4 weeks of the first dose of treatment * Prior treatment with an agent that blocks PD-1/PD-L1 pathway or other immune modulating agents within fewer than 4 weeks of 4 half-lives * Has a diagnosis of immunodeficiency or is receiving any systemic steroid therapy or any form of immunosuppressive therapy within 7 days prior to day 1 of trial treatment * Has had a prior monoclonal antibody within 4 weeks prior to study day 1 or who has not recovered (i.e., ≤ grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier * Has had prior treatment with idelalisib * Has had prior or current treatment with Androgen Deprivation Therapy * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., ≤ grade 1 or at baseline) from adverse events due to a previously administered agent * Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Note: Subjects with ≤ grade 2 neuropathy are an exception to this criterion and may qualify for the study * Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial urothelial cancer, or superficial bladder cancer that has undergone potentially curative therapy * Has an active autoimmune disease requiring systemic treatment within the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs) or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents * Has evidence of interstitial lung disease, active, non-infectious pneumonitis * Has evidence of significant liver disease * Has an active infection requiring systemic therapy; prior to dosing with REGN2810 the subject must be at least 5 half-lives from their last dose of antibiotic * Has a history of listeriosis or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Has a contraindication to administration of amoxicillin, ampicillin, ciprofloxacin, erythromycin, gentamycin, penicillin, trimethoprim/sulfamethoxazole, and vancomycin * Is expecting to spontaneously conceive or father children within the projected duration of the trial, starting with the screening visit through 120 days after the last dose of trial treatment * Has contraindication to administration of non-steroidal anti-inflammatory drugs (NSAIDS) * Is or has an immediate family member (spouse or children) who is investigational site or staff directly involved with this trial, unless prospective Institutional Review Board (IRB) approval (by chair or designee) is given allowing exception to this criterion for a specific subject